Murat Uney

Regional Variance for Multi-Object Filtering

Recent progress in multi-object filtering has led to algorithms that compute the first-order moment of multi-object distributions based on sensor measurements. The number of targets in arbitrarily selected regions can be estimated using the first-order moment. In this work, we introduce explicit formulae for the computation of the second-order statistic on the target number. The proposed concept of regional variance quantifies the level of confidence on target number estimates in arbitrary regions and facilitates information-based decisions. We provide algorithms for its computation for the probability hypothesis density (PHD) and the cardinalized probability hypothesis density (CPHD) filters. We demonstrate the behaviour of the regional statistics through simulation examples.

Graphical Model-based Approaches to Target Tracking in Sensor Networks: An Overview of Some Recent Work and Challenges

Sensor networks have provided a technology base for distributed target tracking applications among others. Conventional centralized approaches to the problem lack scalability in such a scenario where a large number of sensors provide measurements simultaneously under a possibly non-collaborating environment. Therefore research efforts have focused on scalable, robust, and distributed algorithms for the inference tasks related to target tracking, i.e. localization, data association, and track maintenance. Graphical models provide a rigorous tool for development of such algorithms modeling the information structure of a given task and providing distributed solutions through message passing algorithms. However, the limited communication capabilities and energy resources of sensor networks pose the additional difficulty of considering the trade-off between the communication cost and the accuracy of the result. Also the network structure and the information structure are different aspects of the problem and a mapping between the physical entities and the information structure is needed. In this paper we discuss available formalisms based on graphical models for target tracking in sensor networks with a focus on the aforementioned issues. We point out additional constraints that must be asserted in order to achieve further insight and more effective solutions.

Cooperative sensor localisation in distributed fusion networks by exploiting non-cooperative targets

We consider geographically dispersed and networked sensors collecting measurements from multiple targets in a surveillance region. Each sensor node filters the set of cluttered, noisy target measurements it collects in a sensor centric coordinate system and with imperfect detection rates. The filtered multi-target information is, then, communicated to the nearest neighbours. We are interested in network self-localisation in scenarios in which the network is restricted to use only the multi-target information shared. We propose an online distributed sensor localisation scheme based on a pairwise Markov Random Field model of the problem. We first introduce parameter likelihoods for pairs of sensors-equivalently, edge potentials- which can be computed using only the incoming multi-target information and local measurements. Then, we use belief propagation with the associated posterior model which is Markov with respect to the underlying communication topology. We demonstrate the efficacy of our algorithm for cooperative sensor localisation through an example with complex measurement models.

A Cooperative Approach to Sensor Localisation in Distributed Fusion Networks

We consider self-localisation of networked sensor platforms, which are located disparately and collect cluttered and noisy measurements from an unknown number of objects (or, targets). These nodes perform local filtering of their measurements and exchange posterior densities of object states over the network to improve upon their myopic performance. Sensor locations need to be known, however, in order to register the incoming information in a common coordinate frame for fusion. In this work, we are interested in scenarios in which these locations need to be estimated solely based on the multi-object scene. We propose a cooperative scheme which features nodes using only the information they already receive for distributed fusion: we first introduce node-wise separable parameter likelihoods for sensor pairs, which are recursively updated using the incoming multi-object information and the local measurements. Second, we establish a network coordinate system through a pairwise Markov random field model which has the introduced likelihoods as its edge potentials. The resulting algorithm consists of consecutive edge potential updates and Belief Propagation message passing operations. These potentials are capable of incorporating multi-object information without the need to find explicit object-measurement associations and updated in linear complexity with the number of measurements. We demonstrate the efficacy of our algorithm through simulations with multiple objects and complex measurement models.

Maximum Likelihood Signal Parameter Estimation via Track Before Detect

In this work, we consider the front-end processing for an active sensor. We are interested in estimating signal amplitude and noise power based on the outputs from filters that match transmitted waveforms at different ranges and bearing angles. These parameters identify the distributions in, for example, likelihood ratio tests used by detection algorithms and characterise the probability of detection and false alarm rates. Because they are observed through measurements induced by a (hidden) target process, the associated parameter likelihood has a time recursive structure which involves estimation of the target state based on the filter outputs. We use a track-before-detect scheme for maintaining a Bernoulli target model and updating the parameter likelihood. We use a maximum likelihood strategy and demonstrate the efficacy of the proposed approach with an example.

Target localization in acoustic sensor networks using factor graphs

We consider the problem of localizing targets which act as acoustic sources over a region covered by a sensor network in which each node is equipped with an acoustic intensity sensor. The a posteriori distribution of each target location is constructed through a message passing algorithm on the factor graph representation of the joint posterior which is based on the loopy sum product algorithm. After constructing the posteriors, it is possible to compute the MAP or MMSE estimation expressions of the target locations under these distributions. This approach is the application of an information architecture for distributed inference proposed before. Therefore it is naturally amenable to a distributed implementation and depending on functions which can be easily generated, it has the advantage of compliance with the requirements of sensor networks.

Target aided online sensor localisation in bearing only clusters

In this work, we consider a network of bearing only sensors in a surveillance scenario. The processing of target measurements follow a two-tier architecture: The first tier is composed of centralised processing clusters whereas in the second tier, cluster heads perform decentralised processing. We are interested in the first tier problem of locating peripheral sensors relative to their cluster head. We mainly exploit target measurements received by the cluster head in a parameter estimation setting which involves Sequential Monte Carlo methods, and is known to have many difficulties in practice, including particle deficiency, sensitivity to initialisation, and high computational complexity. These difficulties are exacerbated by the bearing-only modality which provides a relatively poor target observability. We propose an online solution through Bayesian recursions on Junction Tree models of the posterior which partition the problem into fixed size subproblems and hence provides scalability with the number of sensors. We use the received signal strength as noisy range measurements to improve the robustness and accuracy of our algorithm. We demonstrate its efficacy with an example.

An efficient Monte Carlo approach for optimizing decentralized estimation networks constrained by undirected topologies

We consider a decentralized estimation network subject to communication constraints such that nearby platforms can communicate with each other through low capacity links rendering an undirected graph. After transmitting symbols based on its measurement, each node outputs an estimate for the random variable it is associated with as a function of both the measurement and incoming messages from neighbors. We are concerned with the underlying design problem and handle it through a Bayesian risk that penalizes the cost of communications as well as estimation errors, and constraining the feasible set of communication and estimation rules local to each node by the undirected communication graph. We adopt an iterative solution previously proposed for decentralized detection networks which can be carried out in a message passing fashion under certain conditions. For the estimation case, the integral operators involved do not yield closed form solutions in general so we utilize Monte Carlo methods. We achieve an iterative algorithm which yields an approximation to an optimal decentralized estimation strategy in a person by person sense subject to such constraints. In an example, we present a quantification of the trade-off between the estimation accuracy and cost of communications using the proposed algorithm.

Detection of Manoeuvring Low SNR Objects in Receiver Arrays

In this work, we are interested in detecting manoeuvring objects in high noise background using an active sensor with a uniform linear array (ULA) receiver and propose a joint pulse integration and trajectory estimation algorithm. This algorithm allows us to detect low SNR objects by integrating multiple pulse returns while taking into account the possibility of object manoeuvres. In the proposed algorithm, the detection is performed by a Neyman-Pearson test, i.e., a likelihood ratio test. The likelihood function used in this test accommodates the radar ambiguity function evaluated in accordance with object related parameters such as location, velocity and reflection coefficient. The trajectory estimation is performed by Bayesian recursive filtering based on the state model of the location and velocity parameters. The reflection coefficient is estimated by a maximum likelihood (ML) estimator. These estimates are used in pulse integration, leading to coherent integration during a coherent processing interval (CPI) and non-coherent integration across consecutive CPIs. We also compare the proposed algorithm with conventional techniques.

Monte Carlo Optimization of Decentralized Estimation Networks Over Directed Acyclic Graphs Under Communication Constraints

Motivated by the vision of sensor networks, we consider decentralized estimation networks over bandwidth-limited communication links, and are particularly interested in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We employ a class of in-network processing strategies that admits directed acyclic graph representations and yields a tractable Bayesian risk that comprises the cost of communications and estimation error penalty. This perspective captures a broad range of possibilities for processing under network constraints and enables a rigorous design problem in the form of constrained optimization. A similar scheme and the structures exhibited by the solutions have been previously studied in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization scheme involves integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both the in-network processing strategies and their optimization. The proposed Monte Carlo optimization procedure operates in a scalable and efficient fashion and, owing to the nonparametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk.